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David Sibley asked in his message from Apr 22 1992:

Is there some easy way to identify from the character table record

which columns are inverses of which other columns? I'd like to be able

to do this to, say, compute class multiplication constants

automatically (by a pre-defined function) from the table. Everything

else needed seems to be readily available in the record.

There is a GAP function 'InverseClassesCharTable' that returns a list

where at position <i> the position of the inverse class of class <i>

is stored. The power maps of the table are in general not sufficient

to compute the inverse classes, so this is done using the 'irreducibles'

component of the table record. We do not store this information on the

table, and do not use it (although it could be used for example by the

scalar product) in order to avoid inconsistencies between character values

and a list of inverses computed at an earlier stage.

Class multiplication constants, or matrices of them, can be computed using

'ClassMultCoeffCharTable' and 'MatClassMultCoeffsCharTable'.

Thomas Breuer

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